How to set transparent pixel in UV
Assuming you're using Eevee:

Per my comment, I think the problem is that your PNG's alpha channel (the second output in your Texture Input node) is not being used to do anything, and Toon BSDF interprets the fully Transparent pixels as black by default. Because of this, I get the same problem with this image of mine, where everything Black is actually Transparent (pixels with alpha=0):



We can fix this by setting Material->Blend Mode to Alpha clip (this assumes you have already set Context->Render Engine->Eevee), Context->Film->Transparent, and using a slightly more complicated shader, which uses our PNG's alpha channel to explicitly control the mix factor between a Transparent BSDF and the color information in our Toon BSDF:



Note that the math node could also be deleted if you switched the order of the inputs to the Mix Shader node.